1074
J. Org. Chem. 1995,60, 1074-1076
Ab Initio Conformational Analysis of truns-Cyclohexene Richard P. Johnson* and Kenneth J. DiRico Department of Chemistry, University of New Hampshire, Durham, New Hampshire 03824 Received August 19, 1994
Introduction The constraint of trans-disubstituted carbon-carbon double bonds in progressively smaller rings engenders large incremental increases in strain and reactivity.l trans-Cyclooctene is an isolable substance,2 while the next smaller homologue trans-cycloheptene has been seen only by low temperature NMR spectro~copy.~Flash spectroscopic experiments have provided the only direct experimental evidence for the existence of trans-cyclohexenes, which have been postulated as transient intermediates in many photoreaction^.^ trans-Cyclopentene is presumably highly strained and has received very little serious c~nsideration.~ Early force field and ab initio computational studies on trans-cyclohexene considered only a single chairlike conformati~n.~,~ During the course of a n ab initio computational study on trans-cyclohexenones, we located two distinct conformational minima, best described as chair and twist-boat.8 At about the same time there appeared reports of a stochastic MM3 (92) conformational search, complementary HF/6-3lG* optimizationsg , and semiempirical calculations1° which led to the same conclusion for trans-cyclohexene. In these studies, only the minima were located. Strained sc bonds and especially transition states for sc bond rotation are not adequately described at the Hartree-Fock (HF) level because of their substantial diradical character. Two configuration SCF (TCSCF) methods which mix (d2and (n*I2configurations provide (1)For general discussions of trans-cycloalkenes, see: (a)Liebman, J. F.; Greenberg, A. Strained Organic Molecules; Academic Press Inc.: New York, 1978.(b) Leuf, W.; Keese, R. Top. Stereochem. 1991,20, 231.(c) Johnson, R.P. in Molecular Structure and Energetics; Liebman, J. F., Greenberg, A., Eds.; VCH Publishers, Inc.: New York, 1986, Chapter 3, p 85.(d) Marshall, J. A. Acc. Chem. Res. 1980,13,213.(e) Warner, P. M. Chem. Rev. 1989,89,1067. (2)Ziegler, K.;Wilms, H. Ann. 1950,567,1.See also references in ref 1. (3) Wallraff, G. M.; Michl, J. J. Org. Chem. 1986,51, 1794. (4)For examples of photochemical reactions that may involve transcyclohexenes, see: (a) Kropp, P. J.; Fravel Jr., H. G.; Fields, T. R. J. Am. Chem. SOC. 1976,981,840. (b) Goodman, J. L.; Peters, K. S.; Misawa, H.; Caldwell, R. A. J. Am. Chem. SOC. 1986,108,6803. (c) Dauben, W. G.; vanRiel, H. C. H. A.; Robbins, J. D.; Wagner, G. J. J. Am. Chem. SOC.1979, 101, 6383. (d) Saltiel, J.; Marchand, G . R.; Bonneau, R. J. Photochem. 1985,28, 367.(e) Inoue, Y.;Matsumoto, (0 Inoue, N.; Hakushi, T.; Srinivasan, R. J. Org. Chem. 1981,46,2267. Y.; Takamuku, S.; Sakurai, H. J. Chem. SOC.Perkin Trans. 2 1977, 1635.(g)Caldwell, R. A.; Misawa, H.; Healy, E. F.; Dewar, M. J. S. J. Am. Chem. SOC. 1987,109,6869. (5)We are aware of no evidence for trans-cyclopentene. For brief discussions, see ref le. Photochemical reactions of cyclopentene do not provide evidence for trans-cyclopentene: Inoue, Y.; Mukai, T.; Hakushi, T. Chem. Lett. 1982,1045. (6)Verbeek, J.; van Lenthe, J. H.; Timmermans, P. J. J. A.; Mackor, A.; Budzelaar, P. H. M. J. Org. Chem. 1987,52,2955. (7)Allinger, N. L.; Sprague, J. T. J.Am. Chem. SOC.1972,94,5734. (8)Johnson, R. P.; Schuster, D. I. Unpublished results. (9)Saunders, M.; JimBnez-Vdsquez, H. A. J. Comput. Chem. 1993, 14,330. (IO)Strickland, A. D.; Caldwell, R. A. J. Phys. Chem. 1993,97, 13394.We thank Professor Caldwell for a preprint of this paper.
an optimal wavefunction for these unusual species.ll We describe here results of a TCSCF/6-31G* study on transcyclohexene in which the three relevant minima and three connecting transition states have been located at the TCSCF/6-31G* level.12 For highly strained species such as these, the barriers to sc bond rotation may be of the same magnitude as those for conformational interconversion. Our calculations provide the most complete analysis to date of the conformations of trans-cyclohexene and their potential for interconversion, both with the cis isomer and with each other.
Computational Methods Structures were initially constructed and minimized at the HF/3-21G level with SPARTAN.13 Successive TCSCF/3-21G and TCSCF/6-31G* geometry optimizations were then performed with GAMESS.14 In all cases, the TCSCF wave function included one orbital of A symmetry and one of B symmetry; these correspond to sc and sc* molecular orbitals. In several cases, TCSCF convergence problems required initial use of MCSCF(2,2) methods to obtain a converged wave function. Analytic hessian calculation and frequency analysis were performed at the TCSCF/3-21G level. Further TCSCF/631G* optimization afforded only minor changes in structures and energetics. All optimizations were restricted to CZsymmetry; vibrational frequency analysis showed this was not an artificial constraint since all stationary points showed the expected number of imaginary frequencies. The TCSCF methodology was calibrated by calculation of the n bond rotational barrier in ethylene.'l* TCSCF/ 6-31G* optimization of both D 2 h and D M structures for ethylene yielded total energies of -78.06026 and -77.95571 hartrees, respectively. This gives a predicted enthalpic barrier of 65.6 kcavmol, which is in excellent agreement with experiment.15 Thus, we have confidence that our predicted barriers should be accurate to within a few kcal/mol.
Results of Calculations Scheme 1provides the most concise pictorial summary of this work. All structures shown are from TCSCF/631G* optimizations. Relative energies (kcaYmo1) in Scheme 1are given a t the TCSCF/6-31G*level, corrected with zero point differences calculated at the TCSCF/321G level. Total and relative energies calculated at all levels are given in Table 1. The HF/3-21G energies for 2 and 3 are ca. 10 kcallmol above the TCSCF values; this is readily attributed to the biradical character in the (11)(a) Wood, M. W. Chem. Phys. Lett. 1974,24,239. This paper reports TCSCFDZ calculations on the rotational barrier in ethylene. (b) Borden, W. T., Chem. Rev. 1989,89,1045. (12)For recent studies on the conformational analysis of ciscyclohexene, see: (a) Laane, J.; Choo, J. J.Am. Chem. SOC.1994,116, 3889.(b) Anet, F. A. L.; Freedberg, D. I.; Stover, J. W.; Houk, K. N. J. Am. Chem. SOC. 1992, 114 , 10969. (c) Anet, F. A. L. in The Conformational Analysis of Cyclohexenes, Cyclohexadienesand Related Hydroaromatic Compounds; Rabideau, P. W., Ed., VCH Publishers: New York, 1987;Chpt. 1. (13)SPARTAN, Version 3.0,Wavefunction Inc., 1993. (14)GAIvlESS: Schmidt, M. W.; Baldridge, K. K.; Boatz, J . A.; Jensen, J. H.; Koseki, S.; Gordon, M. S.;Nguyen, K. A.; Windus, T. L.; Elbert, S. T. QCPE Bull. 1990,10,52. (15) Douglas, J. E.; Rabinovitch, B. S.; Looney, F. S. J. Chem. Phys. 1955,23,315.
0022-3263/95/1960-1074$09.00/0 0 1995 American Chemical Society
Notes
J. Org. Chem., Vol. 60, No. 4, 1995 1075
Scheme 1. Structures a n d Relative Energies (kcavmol) for trans-Cyclohexene Conformers and Transition States
2 (59.3)
3 (54.7)
1 (0.0 kcal/mol)
Table 1. Energetics of transCyclohexene Conformers and Transition States*.* structure cyclohexene 11)(half-chair) twist-boat trans-cyclohexene(2) chair trans-cyclohexene 13) twist-boat bond transition state (4TS) chair R bond transition state l5TS) chair ta twist-boat transition state (6TS)
HF/3-21G -231.72915 -231.61802 -231.62798 d d -231.61671
(0.0) (69.7) (63.5) (70.6)
TCSCF/3-21G -231.75773 -231.66434 -231.67309 -231.64305 -231.65007 -231.66434
(0.0) (58.6) (53.1) (72.0)
(67.6) (62.3)
TCSCF/6-31G* -233.04672 -232.95076 -232.95872 -232.93072 -232.93794 -232.94794
10.0) 160.2) 155.2) (72.8) (68.3) (62.0)
ZPVEc 98.1 97.2 97.6 94.8 Iv, = -895.8 95.1 /vi = -872.81 97.2 [VI = -200.51
Total energies in hartrees. Relative energies (kcalimol) are given in parentheses. All structures were optimized within C2 symmetry a t the computational level cited. In k c a h " , calculated a t the TCSCFIS-2lG level with unsealed frequencies. HF level calculation is not appropriate for this species.
Table 2. Selected Structural Data from
a recent study by Caldwell and co-workers who used photoacoustic calorimetry to measure a trans-cis isomerization energy of either 44.7 f 5 or 47.0 f 3 kcalimol for double bond dihedral angle dihedral angle structure length, 8, H-C=C-H, deg C-C=C-C, deg l-phenylcy~lohexene.~~J~ 1 1.341 1.7 -0.316 Trans isomer 3 has two available reaction paths: II 2 1.381 174.6 8R.l bond rotation to 1 which has a predicted barrier of 10.6 kcavmol, and interconversion with the twist-boat conformer, with a barrier of 6.4 kcaWmo1. In the opposite direction, twist-boat conformer 2 has a 10.2 kcaWmol barrier for n bond rotation, but a barrier of only 1.8 kcal! mol for isomerization to 3. Thus, within its short lifetime, trans structures. Selected geometric parameters are prior to n bond rotation, 3 should undergo a rapid, but collected in Table 2. conformationally biased, interconversion with 2, while 2 Structure 1 is the well-known half-chair conformation should easily convert to 3. Caldwell and co-workers4c ofcis-cyclohexene12while 2 and 3 are the twist-boat and have chair conformers, respectively, for t r a n s - c y c l ~ h e x e n e . ~ ~ ~ ~ measured a 12.1 kcaWmol barrier for trans to cis isomerization of 1-phenylcyclohexene. In principle, phenThe two transition states for n bond rotation to 1 are yl substitution should diminish the barrier, thus our shown as 4TS and 5TS, while 6TS is the transition state predicted barrier of 10.6 kcaWmol appears to be a few for conformational interconversion between chair and kcaWmol too low. twist-boat. The structures of 2 and 3 show only slightly elongated We first consider the relative energetics and most likely n bonds (Table 2) which are substantially pyramidalized. pathways available to these reactive species. Our calThus, while the H-C=C-H dihedral angles for 2 and 3 culations concur with earlier studiesgJOin predicting that are close to 180", the C-C=C-C angles are nearly the chair conformer 3 should be the lowest energy form orthogonal. For the n bond transition states 4TS and of trans-cyclohexene. The chair to twist-boat energy 5TS, these values show a clear progression toward 1. differenceis about the same as that for the corresponding conformers of cyclohexane. This structure permits a fully Efforts with a TCSCF/3SlG wave function to locate a trans double bond while still minimizing other forms of minimum corresponding to trans-cyclopentene (7)have strain. Chair structure 3 is predicted t o be 54.7 kcall been unsuccessful to date. Simple extrapolation from the mol above cis-1; this value agrees well with previous present results, as well as data on larger ring homologues,',I0 suggest that if it exists, the n bond strain e s t i m a t e ~ . ~ J .Relevant ~J~ experimental data come from TCSCF/6-31GLOptimizations
1076
J. Org. Chem., VoZ.60, No. 4, 1995
energy of 7 should be ’70 kcdmol. Nevertheless, we believe it is possible that a shallow minimum exists for 7, and we are continuing efforts to locate this structure.
Conclusions Our calculations support the existence of two conformational minima for trans-cyclohexene. This result is in agreement with other recent st~dies.~JO However, we find that the twist-boat structure 2 is of sufficiently higher energy and has such a small barrier to conformational change that it may not play a significant role in the chemistry of these strained species. In each case, n bond rotation has a predicted barrier of ca. 10 kcdmol, and rotation should lead to 1 since there appear to be no other low energy minima for cyclohexene.12 We believe the value of this conformational analysis may lie in the eventual ability to “tune” these processes by ring substituents or other structural modifications, much as has been done for cyclohexanes. trans-Cyclohexenones are potential intermediates in cyclohexenone photochemistry16and we are currently studying the role of conformational control in trans-intermediates as one
Notes explanation of the diverse photochemical reactions of cyclohexenones. We are also studying the unusually large secondary kinetic isotope effects ( k ~ l for k ~ vinyl deuterium) that have been observed for trans to cis isomerization in phenylcy~lohexene.~g
Acknowledgment. We are grateful to the National Science Foundation for support of this research, to the Pittsburgh Supercomputing Center for an allocation of CPU time, and to Professor David Schuster for stimulating our interest in this problem. Supplementary Material Available: Cartesian coordinates (A) for TCSCF/6-31G* stationary points calculated in this research (6 pages). This material is contained in libraries on microfiche, immediately follows this article in the microfilm version of the journal, a n d can be ordered from the ACS; see any current masthead page for ordering information.
509414412 ~~~~
~
~
~
~
(16)Review: Schuster, D. I. in The Chemistry ofEnones; Patai, S., Rappoport, Z., Eds.,John Wiley & Sons: New York, 1989.
